An efficient approach for the calculation of frequencies in macromolecules

I. INTRODUCTION. Conformational changes of macromolecules are essential in the understanding of e.g. proteins and drug design. The theoretical prediction is far from trivial, especially for large molecules. In many cases, collective motions are present which occur on a timescale (~ms) that is too long to be accessible through molecular dynamics simulations. Normal mode analysis (NMA) has been proven succesful in exploring the potential energy surface (PES) within the harmonic oscillator approximation. The lowest frequency modes contribute the most to a conformational change. This paper presents a computationally attractive method that selects modes from the lower spectrum

Normal mode analysis of macromolecular systems with the Mobile Block Hessian method

Until recently, normal mode analysis (NMA) was limited to small proteins, not only because the required energy minimization is a computationally exhausting task, but also because NMA requires the expensive diagonalization of a 3Na 3Na matrix with Na the number of atoms. A series of simplified models has been proposed, in particular the Rotation-Translation Blocks (RTB) method by Tama et al. for the simulation of proteins. It makes use of the concept that a peptide chain or protein can be seen as a subsequent set of rigid components, i.e. the peptide units. A peptide chain is thus divided into rigid blocks with six degrees of freedom each. Recently we developed the Mobile Block Hessian (MBH) method, which in a sense has similar features as the RTB method. The main difference is that MBH was developed to deal with partially optimized systems. The position/orientation of each block is optimized while the internal geometry is kept fixed at a plausible – but not necessarily optimized – geometry. This reduces the computational cost of the energy minimization. Applying the standard NMA on a partially optimized structure however results in spurious imaginary frequencies and unwanted coordinate dependence. The MBH avoids these unphysical effects by taking into account energy gradient corrections. Moreover the number of variables is reduced, which facilitates the diagonalization of the Hessian. In the original implementation of MBH, atoms could only be part of one rigid block. The MBH is now extended to the case where atoms can be part of two or more blocks. Two basic linkages can be realized: (1) blocks connected by one link atom, or (2) by two link atoms, where the latter is referred to as the hinge type connection. In this work we present the MBH concept and illustrate its performance with the crambin protein as an example

Direct and indirect lactate oxidation in trained and untrained men.

Lactate has been shown to be an important oxidative fuel. We aimed to quantify the total lactate oxidation rate (Rox) and its direct vs. indirect (glucose that is gluconeogenically derived from lactate and subsequently oxidized) components (mg·kg(-1)·min(-1)) during rest and exercise in humans. We also investigated the effects of endurance training, exercise intensity, and blood lactate concentration ([lactate]b) on direct and indirect lactate oxidation. Six untrained (UT) and six trained (T) men completed 60 min of constant load exercise at power outputs corresponding to their lactate threshold (LT). T subjects completed two additional 60-min sessions of constant load exercise at 10% below the LT workload (LT-10%), one of which included a lactate clamp (LC; LT-10%+LC). Rox was higher at LT in T [22.7 ± 2.9, 75% peak oxygen consumption (Vo2peak)] compared with UT (13.4 ± 2.5, 68% Vo2peak, P < 0.05). Increasing [lactate]b (LT-10%+LC, 67% Vo2peak) significantly increased lactate Rox (27.9 ± 3.0) compared with its corresponding LT-10% control (15.9 ± 2.2, P < 0.05). Direct and indirect Rox increased significantly from rest to exercise, and their relative partitioning remained constant in all trials but differed between T and UT: direct oxidation comprised 75% of total lactate oxidation in UT and 90% in T, suggesting the presence of training-induced adaptations. Partitioning of total carbohydrate (CHO) use showed that subjects derived one-third of CHO energy from blood lactate, and exogenous lactate infusion increased lactate oxidation significantly, causing a glycogen-sparing effect in exercising muscle

The north–south asymmetry of the ALFALFA H I velocity width function

The number density of extragalactic 21-cm radio sources as a function of their spectral line widths – the H I width function (H I WF) – is a sensitive tracer of the dark matter halo mass function (HMF). The Lambda cold dark matter model predicts that the HMF should be identical everywhere provided it is sampled in sufficiently large volumes, implying that the same should be true of the H I WF. The Arecibo Legacy Fast ALFA (ALFALFA) 21-cm survey measured the H I WF in northern and southern Galactic fields and found a systematically higher number density in the north. At face value, this is in tension with theoretical predictions. We use the Sibelius-DARK N-body simulation and the semi-analytical galaxy formation model GALFORM to create a mock ALFALFA survey. We find that the offset in number density has two origins: the sensitivity of the survey is different in the two fields, which has not been correctly accounted for in previous measurements; and the 1/Veff algorithm used for completeness corrections does not fully account for biases arising from spatial clustering in the galaxy distribution. The latter is primarily driven by a foreground overdensity in the northern field within 30 Mpc , but more distant structure also plays a role. We provide updated measurements of the ALFALFA H I WF (and H I mass function) correcting for the variations in survey sensitivity. Only when systematic effects such as these are understood and corrected for can cosmological models be tested against the H I WF

On the development of a partial vibrational analysis within a QM/MM approach

In molecular modeling extended systems are often only partially optimized in order to restrict the computational cost. For instance in a first step the whole system is optimized at a low level-of-theory, and in the next step only part of the atoms, usually the chemically active region, is optimized at a high level-of-theory, while atoms in the passive region are kept fixed at their original positions. However, partially optimized geometries are non-equilibrium structures and the standard normal mode analysis (NMA) shows some serious defects, e.g. spurious imaginary frequencies may appear. In the Partial Hessian Vibrational Analysis [1],[2] these defects are surmounted by giving the fixed part an infinite mass. We propose a new model, the Mobile Block Hessian (MBH) approach, which takes into account the finite mass of the fixed block and avoids the spurious frequencies and the coordinate dependence [3]. The approach was generalized to the case of several mobile blocks. The MBH has been validated by comparing eigenfrequencies and eigenvectors, vibrational entropy and enthalpy, and recently reaction rate constants [4], with remarkably satisfying results. One of the main advantages is that the implementation of the MBH allows a considerable reduction of computer time [5]. After several tests with smaller QM systems, the method is now also included in the CHARMM package, allowing the simulation of more extended (bio)systems. The next step is combining the MBH approach with QM/MM, currently in a developing stage, which will broaden the range of applications. MBH in QM/MM is a very promising methodology for extended systems. Whereas a full normal mode analysis is unfeasible even if only the MM part of the system increases, because of the high number of expensive second derivatives of the QM/MM interaction terms in the Hamiltionian, the MBH can considerably reduce this cost, thereby opening the path to vibrational analysis in extended QM/MM systems. [1] J. D. Head, Int. J. of Quantum Chem. 65, 827 (1997) [2] H. Li and J. H. Jensen, Theor. Chem. Accounts. 107(4): 211-219 (2002) [3] A. Ghysels, D. Van Neck, V. Van Speybroeck, T. Verstraelen, M. Waroquier, J. Chem. Phys. 126, 224102 (2007) [4] A. Ghysels, V. Van Speybroeck, T. Verstraelen, D. Van Neck, M. Waroquier, J. Chem. Theor. Comp. 4 (4), 614-625 (2008) [5] A. Ghysels, D. Van Neck, M. Waroquier, J. Chem. Phys. 127, 164108 (2007

Normal mode analysis of macromolecular systems with the mobile block Hessian method

Until recently, normal mode analysis (NMA) was limited to small proteins, not only because the required energy minimization is a computationally exhausting task, but also because NMA requires the expensive diagonalization of a 3N(a) x 3N(a) matrix with N-a the number of atoms. A series of simplified models has been proposed, in particular the Rotation-Translation Blocks (RTB) method by Tama et al. for the simulation of proteins. It makes use of the concept that a peptide chain or protein can be seen as a subsequent set of rigid components, i.e. the peptide units. A peptide chain is thus divided into rigid blocks with six degrees of freedom each. Recently we developed the Mobile Block Hessian (MBH) method, which in a sense has similar features as the RTB method. The main difference is that MBH was developed to deal with partially optimized systems. The position/orientation of each block is optimized while the internal geometry is kept fixed at a plausible - but not necessarily optimized - geometry. This reduces the computational cost of the energy minimization. Applying the standard NMA on a partially optimized structure however results in spurious imaginary frequencies and unwanted coordinate dependence. The MBH avoids these unphysical effects by taking into account energy gradient corrections. Moreover the number of variables is reduced, which facilitates the diagonalization of the Hessian. In the original implementation of MBH, atoms could only be part of one rigid block. The MBH is now extended to the case where atoms can be part of two or more blocks. Two basic linkages can be realized: (1) blocks connected by one link atom, or (2) by two link atoms, where the latter is referred to as the hinge type connection. In this work we present the MBH concept and illustrate its performance with the crambin protein as an example